AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
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DOI：
10.1070/im1987v029n01abeh000958
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发表时间：
1987-02
期刊：
影响因子：
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通讯作者：
V. Zhikov
中科院分区：
文献类型：
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作者：
V. Zhikov
发展了非线性变分问题平均理论中的对偶方法。讨论的一般性问题包括对正则性概念的详细分析、非正则拉格朗日的例子以及考虑正则性问题的对偶公式的推导。主要内容涉及随机拉格朗日变分问题的平均。研究了三组问题：1）一般形式的拉格朗日函数的平均； 2）塑性拉格朗日的平均（极限载荷理论）； 3) 简并拉格朗日函数的平均（随机软或刚性夹杂物的问题）。参考书目：13 种。
Duality methods in the theory of averaging of nonlinear variational problems are developed. The questions of a general nature that are discussed include a detailed analysis of the concept of regularity, an example of a nonregular Lagrangian, and the derivation of duality formulas that take account of the regularity problem. The main content is concerned with the averaging of variational problems with stochastic Lagrangians. Three groups of questions are investigated: 1) averaging of Lagrangians of a general form; 2) averaging of the Lagrangians of plasticity (the theory of the limit load); and 3) averaging of degenerate Lagrangians (problems with random soft or rigid inclusions). Bibliography: 13 titles.